I've never been to Korea, but they do not eat pets. They eat a certain breed of dog that is raised as food. It's not something I would purposely go out to eat myself if I ever end up visiting Korea, but it's not something I am opposed to.

Similarly, I live in Japan and people here are revolted when I say that I've eaten rabbits. It's because their perception of rabbits are the cute, cuddly, useless pets that everyone adores. They have no concept of a long-eared desert hare from Arizona. If I say that I've eaten rabbit, they think of me eating their precious little pet. Not so. I dunno about China though. They'll eat anything that moves.